TSTP Solution File: REL044+2 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : REL044+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.GKeEiOTyDp true
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:47:30 EDT 2023
% Result : Theorem 76.18s 11.57s
% Output : Refutation 76.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 26
% Syntax : Number of formulae : 239 ( 226 unt; 11 typ; 0 def)
% Number of atoms : 230 ( 229 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 1285 ( 3 ~; 0 |; 0 &;1280 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 293 ( 0 ^; 293 !; 0 ?; 293 :)
% Comments :
%------------------------------------------------------------------------------
thf(sk__1_type,type,
sk__1: $i ).
thf(join_type,type,
join: $i > $i > $i ).
thf(converse_type,type,
converse: $i > $i ).
thf(sk__type,type,
sk_: $i ).
thf(meet_type,type,
meet: $i > $i > $i ).
thf(sk__2_type,type,
sk__2: $i ).
thf(top_type,type,
top: $i ).
thf(zero_type,type,
zero: $i ).
thf(composition_type,type,
composition: $i > $i > $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(one_type,type,
one: $i ).
thf(maddux1_join_commutativity,axiom,
! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ) ).
thf(zip_derived_cl0,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(def_top,axiom,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ) ).
thf(zip_derived_cl11,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(maddux2_join_associativity,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ) ).
thf(zip_derived_cl1,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[maddux2_join_associativity]) ).
thf(zip_derived_cl38,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ ( join @ ( complement @ X1 ) @ X0 ) )
= ( join @ top @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl1]) ).
thf(composition_identity,axiom,
! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ) ).
thf(zip_derived_cl5,plain,
! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ),
inference(cnf,[status(esa)],[composition_identity]) ).
thf(converse_idempotence,axiom,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ) ).
thf(zip_derived_cl7,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(converse_multiplicativity,axiom,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X0 @ X1 ) )
= ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ) ).
thf(zip_derived_cl9,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X1 @ X0 ) )
= ( composition @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_multiplicativity]) ).
thf(zip_derived_cl25,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ ( converse @ X0 ) @ X1 ) )
= ( composition @ ( converse @ X1 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl9]) ).
thf(zip_derived_cl210,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= ( composition @ ( converse @ one ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl5,zip_derived_cl25]) ).
thf(zip_derived_cl7_001,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl217,plain,
! [X0: $i] :
( X0
= ( composition @ ( converse @ one ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl210,zip_derived_cl7]) ).
thf(zip_derived_cl5_002,plain,
! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ),
inference(cnf,[status(esa)],[composition_identity]) ).
thf(composition_associativity,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
= ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ) ).
thf(zip_derived_cl4,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
= ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[composition_associativity]) ).
thf(zip_derived_cl120,plain,
! [X0: $i,X1: $i] :
( ( composition @ X0 @ ( composition @ one @ X1 ) )
= ( composition @ X0 @ X1 ) ),
inference('sup+',[status(thm)],[zip_derived_cl5,zip_derived_cl4]) ).
thf(zip_derived_cl226,plain,
! [X0: $i] :
( ( composition @ one @ X0 )
= ( composition @ ( converse @ one ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl217,zip_derived_cl120]) ).
thf(zip_derived_cl217_003,plain,
! [X0: $i] :
( X0
= ( composition @ ( converse @ one ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl210,zip_derived_cl7]) ).
thf(zip_derived_cl232,plain,
! [X0: $i] :
( ( composition @ one @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl226,zip_derived_cl217]) ).
thf(converse_cancellativity,axiom,
! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ X1 ) ) ) @ ( complement @ X1 ) )
= ( complement @ X1 ) ) ).
thf(zip_derived_cl10,plain,
! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X1 ) @ ( complement @ ( composition @ X1 @ X0 ) ) ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(cnf,[status(esa)],[converse_cancellativity]) ).
thf(zip_derived_cl276,plain,
! [X0: $i] :
( ( join @ ( composition @ ( converse @ one ) @ ( complement @ X0 ) ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl232,zip_derived_cl10]) ).
thf(zip_derived_cl217_004,plain,
! [X0: $i] :
( X0
= ( composition @ ( converse @ one ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl210,zip_derived_cl7]) ).
thf(zip_derived_cl5_005,plain,
! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ),
inference(cnf,[status(esa)],[composition_identity]) ).
thf(zip_derived_cl227,plain,
( one
= ( converse @ one ) ),
inference('sup+',[status(thm)],[zip_derived_cl217,zip_derived_cl5]) ).
thf(zip_derived_cl232_006,plain,
! [X0: $i] :
( ( composition @ one @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl226,zip_derived_cl217]) ).
thf(zip_derived_cl277,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl276,zip_derived_cl227,zip_derived_cl232]) ).
thf(zip_derived_cl11_007,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl1_008,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[maddux2_join_associativity]) ).
thf(zip_derived_cl35,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ ( join @ X0 @ ( complement @ ( join @ X1 @ X0 ) ) ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl1]) ).
thf(zip_derived_cl1246,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( join @ ( complement @ X0 ) @ ( complement @ ( complement @ X0 ) ) ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl277,zip_derived_cl35]) ).
thf(zip_derived_cl11_009,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl0_010,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl1299,plain,
! [X0: $i] :
( ( join @ top @ ( complement @ X0 ) )
= top ),
inference(demod,[status(thm)],[zip_derived_cl1246,zip_derived_cl11,zip_derived_cl0]) ).
thf(zip_derived_cl35_011,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ ( join @ X0 @ ( complement @ ( join @ X1 @ X0 ) ) ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl1]) ).
thf(zip_derived_cl1346,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1299,zip_derived_cl35]) ).
thf(zip_derived_cl0_012,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl1354,plain,
! [X0: $i] :
( ( join @ top @ X0 )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1346,zip_derived_cl0]) ).
thf(zip_derived_cl1716,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ ( join @ ( complement @ X1 ) @ X0 ) )
= top ),
inference(demod,[status(thm)],[zip_derived_cl38,zip_derived_cl1354]) ).
thf(zip_derived_cl1731,plain,
! [X0: $i,X1: $i] :
( ( join @ X0 @ ( join @ X1 @ ( complement @ X0 ) ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl1716]) ).
thf(goals,conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( ( join @ ( composition @ ( complement @ X0 ) @ X1 ) @ ( complement @ X2 ) )
= ( complement @ X2 ) )
=> ( ( join @ ( composition @ X2 @ ( converse @ X1 ) ) @ X0 )
= X0 ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( ( join @ ( composition @ ( complement @ X0 ) @ X1 ) @ ( complement @ X2 ) )
= ( complement @ X2 ) )
=> ( ( join @ ( composition @ X2 @ ( converse @ X1 ) ) @ X0 )
= X0 ) ),
inference('cnf.neg',[status(esa)],[goals]) ).
thf(zip_derived_cl16,plain,
( ( join @ ( composition @ ( complement @ sk_ ) @ sk__1 ) @ ( complement @ sk__2 ) )
= ( complement @ sk__2 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1_013,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[maddux2_join_associativity]) ).
thf(zip_derived_cl105,plain,
! [X0: $i] :
( ( join @ ( composition @ ( complement @ sk_ ) @ sk__1 ) @ ( join @ ( complement @ sk__2 ) @ X0 ) )
= ( join @ ( complement @ sk__2 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl16,zip_derived_cl1]) ).
thf(zip_derived_cl2983,plain,
( top
= ( join @ ( complement @ sk__2 ) @ ( complement @ ( composition @ ( complement @ sk_ ) @ sk__1 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1731,zip_derived_cl105]) ).
thf(maddux4_definiton_of_meet,axiom,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ) ).
thf(zip_derived_cl3,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl3978,plain,
( ( meet @ sk__2 @ ( composition @ ( complement @ sk_ ) @ sk__1 ) )
= ( complement @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl2983,zip_derived_cl3]) ).
thf(zip_derived_cl11_014,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl3_015,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl114,plain,
! [X0: $i] :
( ( meet @ X0 @ ( complement @ X0 ) )
= ( complement @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl3]) ).
thf(def_zero,axiom,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ) ).
thf(zip_derived_cl12,plain,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_zero]) ).
thf(zip_derived_cl117,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl114,zip_derived_cl12]) ).
thf(zip_derived_cl3988,plain,
( ( meet @ sk__2 @ ( composition @ ( complement @ sk_ ) @ sk__1 ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl3978,zip_derived_cl117]) ).
thf(zip_derived_cl7_016,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(dedekind_law,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) )
= ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) ) ).
thf(zip_derived_cl13,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ X0 @ X2 ) @ X1 ) @ ( composition @ ( meet @ X0 @ ( composition @ X1 @ ( converse @ X2 ) ) ) @ ( meet @ X2 @ ( composition @ ( converse @ X0 ) @ X1 ) ) ) )
= ( composition @ ( meet @ X0 @ ( composition @ X1 @ ( converse @ X2 ) ) ) @ ( meet @ X2 @ ( composition @ ( converse @ X0 ) @ X1 ) ) ) ),
inference(cnf,[status(esa)],[dedekind_law]) ).
thf(zip_derived_cl400,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ X2 @ ( converse @ X0 ) ) @ X1 ) @ ( composition @ ( meet @ X2 @ ( composition @ X1 @ X0 ) ) @ ( meet @ ( converse @ X0 ) @ ( composition @ ( converse @ X2 ) @ X1 ) ) ) )
= ( composition @ ( meet @ X2 @ ( composition @ X1 @ ( converse @ ( converse @ X0 ) ) ) ) @ ( meet @ ( converse @ X0 ) @ ( composition @ ( converse @ X2 ) @ X1 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl13]) ).
thf(zip_derived_cl7_017,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl424,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ X2 @ ( converse @ X0 ) ) @ X1 ) @ ( composition @ ( meet @ X2 @ ( composition @ X1 @ X0 ) ) @ ( meet @ ( converse @ X0 ) @ ( composition @ ( converse @ X2 ) @ X1 ) ) ) )
= ( composition @ ( meet @ X2 @ ( composition @ X1 @ X0 ) ) @ ( meet @ ( converse @ X0 ) @ ( composition @ ( converse @ X2 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl400,zip_derived_cl7]) ).
thf(zip_derived_cl31533,plain,
( ( join @ ( meet @ ( composition @ sk__2 @ ( converse @ sk__1 ) ) @ ( complement @ sk_ ) ) @ ( composition @ zero @ ( meet @ ( converse @ sk__1 ) @ ( composition @ ( converse @ sk__2 ) @ ( complement @ sk_ ) ) ) ) )
= ( composition @ ( meet @ sk__2 @ ( composition @ ( complement @ sk_ ) @ sk__1 ) ) @ ( meet @ ( converse @ sk__1 ) @ ( composition @ ( converse @ sk__2 ) @ ( complement @ sk_ ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3988,zip_derived_cl424]) ).
thf(zip_derived_cl0_018,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl3_019,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl112,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X1 ) @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl3]) ).
thf(zip_derived_cl3_020,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl6063,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( meet @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl112,zip_derived_cl3]) ).
thf(zip_derived_cl1346_021,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1299,zip_derived_cl35]) ).
thf(zip_derived_cl11_022,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl7_023,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(converse_additivity,axiom,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ) ).
thf(zip_derived_cl8,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_additivity]) ).
thf(zip_derived_cl0_024,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl21,plain,
! [X0: $i,X1: $i] :
( ( join @ ( converse @ X0 ) @ ( converse @ X1 ) )
= ( converse @ ( join @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl8,zip_derived_cl0]) ).
thf(zip_derived_cl30,plain,
! [X0: $i,X1: $i] :
( ( join @ ( converse @ X1 ) @ X0 )
= ( converse @ ( join @ ( converse @ X0 ) @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl21]) ).
thf(zip_derived_cl579,plain,
! [X0: $i] :
( ( join @ ( converse @ ( complement @ ( converse @ X0 ) ) ) @ X0 )
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl30]) ).
thf(zip_derived_cl1367,plain,
( top
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1346,zip_derived_cl579]) ).
thf(zip_derived_cl16_025,plain,
( ( join @ ( composition @ ( complement @ sk_ ) @ sk__1 ) @ ( complement @ sk__2 ) )
= ( complement @ sk__2 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0_026,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl104,plain,
( ( join @ ( complement @ sk__2 ) @ ( composition @ ( complement @ sk_ ) @ sk__1 ) )
= ( complement @ sk__2 ) ),
inference('sup+',[status(thm)],[zip_derived_cl16,zip_derived_cl0]) ).
thf(maddux3_a_kind_of_de_Morgan,axiom,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ) ).
thf(zip_derived_cl2,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux3_a_kind_of_de_Morgan]) ).
thf(zip_derived_cl3_027,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl157,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl3]) ).
thf(zip_derived_cl164,plain,
( sk__2
= ( join @ ( meet @ sk__2 @ ( composition @ ( complement @ sk_ ) @ sk__1 ) ) @ ( complement @ ( complement @ sk__2 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl104,zip_derived_cl157]) ).
thf(zip_derived_cl0_028,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl254,plain,
( ( join @ ( complement @ ( complement @ sk__2 ) ) @ ( meet @ sk__2 @ ( composition @ ( complement @ sk_ ) @ sk__1 ) ) )
= sk__2 ),
inference('sup+',[status(thm)],[zip_derived_cl164,zip_derived_cl0]) ).
thf(zip_derived_cl1716_029,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ ( join @ ( complement @ X1 ) @ X0 ) )
= top ),
inference(demod,[status(thm)],[zip_derived_cl38,zip_derived_cl1354]) ).
thf(zip_derived_cl1741,plain,
( ( join @ ( complement @ sk__2 ) @ sk__2 )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl254,zip_derived_cl1716]) ).
thf(zip_derived_cl1_030,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[maddux2_join_associativity]) ).
thf(zip_derived_cl0_031,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl32,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X2 @ X1 ) )
= ( join @ X2 @ ( join @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1,zip_derived_cl0]) ).
thf(zip_derived_cl1762,plain,
! [X0: $i] :
( ( join @ sk__2 @ ( join @ X0 @ ( complement @ sk__2 ) ) )
= ( join @ X0 @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1741,zip_derived_cl32]) ).
thf(zip_derived_cl1346_032,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1299,zip_derived_cl35]) ).
thf(zip_derived_cl1770,plain,
! [X0: $i] :
( ( join @ sk__2 @ ( join @ X0 @ ( complement @ sk__2 ) ) )
= top ),
inference(demod,[status(thm)],[zip_derived_cl1762,zip_derived_cl1346]) ).
thf(zip_derived_cl7_033,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl8_034,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_additivity]) ).
thf(zip_derived_cl23,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X1 @ ( converse @ X0 ) ) )
= ( join @ ( converse @ X1 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl8]) ).
thf(zip_derived_cl23_035,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X1 @ ( converse @ X0 ) ) )
= ( join @ ( converse @ X1 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl8]) ).
thf(zip_derived_cl48,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( converse @ ( join @ X2 @ ( join @ ( converse @ X1 ) @ X0 ) ) )
= ( join @ ( converse @ X2 ) @ ( join @ X1 @ ( converse @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl23,zip_derived_cl23]) ).
thf(zip_derived_cl2398,plain,
! [X0: $i] :
( ( converse @ top )
= ( join @ ( converse @ sk__2 ) @ ( join @ X0 @ ( converse @ ( complement @ sk__2 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1770,zip_derived_cl48]) ).
thf(zip_derived_cl1367_036,plain,
( top
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1346,zip_derived_cl579]) ).
thf(zip_derived_cl2441,plain,
! [X0: $i] :
( top
= ( join @ ( converse @ sk__2 ) @ ( join @ X0 @ ( converse @ ( complement @ sk__2 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2398,zip_derived_cl1367]) ).
thf(zip_derived_cl7_037,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl8_038,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_additivity]) ).
thf(zip_derived_cl24,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ ( converse @ X0 ) @ X1 ) )
= ( join @ X0 @ ( converse @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl8]) ).
thf(zip_derived_cl9_039,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X1 @ X0 ) )
= ( composition @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_multiplicativity]) ).
thf(zip_derived_cl66,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( converse @ ( composition @ X2 @ ( join @ ( converse @ X1 ) @ X0 ) ) )
= ( composition @ ( join @ X1 @ ( converse @ X0 ) ) @ ( converse @ X2 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl24,zip_derived_cl9]) ).
thf(zip_derived_cl4214,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X0 @ top ) )
= ( composition @ ( join @ sk__2 @ ( converse @ ( join @ X1 @ ( converse @ ( complement @ sk__2 ) ) ) ) ) @ ( converse @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2441,zip_derived_cl66]) ).
thf(zip_derived_cl7_040,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl21_041,plain,
! [X0: $i,X1: $i] :
( ( join @ ( converse @ X0 ) @ ( converse @ X1 ) )
= ( converse @ ( join @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl8,zip_derived_cl0]) ).
thf(zip_derived_cl31,plain,
! [X0: $i,X1: $i] :
( ( join @ X0 @ ( converse @ X1 ) )
= ( converse @ ( join @ X1 @ ( converse @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl21]) ).
thf(zip_derived_cl1716_042,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ ( join @ ( complement @ X1 ) @ X0 ) )
= top ),
inference(demod,[status(thm)],[zip_derived_cl38,zip_derived_cl1354]) ).
thf(zip_derived_cl4247,plain,
! [X0: $i] :
( ( converse @ ( composition @ X0 @ top ) )
= ( composition @ top @ ( converse @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4214,zip_derived_cl31,zip_derived_cl1716]) ).
thf(zip_derived_cl7_043,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl4269,plain,
! [X0: $i] :
( ( converse @ ( composition @ top @ ( converse @ X0 ) ) )
= ( composition @ X0 @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl4247,zip_derived_cl7]) ).
thf(zip_derived_cl4436,plain,
( ( converse @ ( composition @ top @ top ) )
= ( composition @ top @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1367,zip_derived_cl4269]) ).
thf(zip_derived_cl9_044,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X1 @ X0 ) )
= ( composition @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
inference(cnf,[status(esa)],[converse_multiplicativity]) ).
thf(zip_derived_cl10_045,plain,
! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X1 ) @ ( complement @ ( composition @ X1 @ X0 ) ) ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(cnf,[status(esa)],[converse_cancellativity]) ).
thf(zip_derived_cl132,plain,
! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ ( converse @ X0 ) ) @ ( complement @ ( converse @ ( composition @ X1 @ X0 ) ) ) ) @ ( complement @ ( converse @ X1 ) ) )
= ( complement @ ( converse @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl9,zip_derived_cl10]) ).
thf(zip_derived_cl7_046,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl0_047,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl137,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ ( converse @ X1 ) ) @ ( composition @ X0 @ ( complement @ ( converse @ ( composition @ X1 @ X0 ) ) ) ) )
= ( complement @ ( converse @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl132,zip_derived_cl7,zip_derived_cl0]) ).
thf(zip_derived_cl8328,plain,
( ( join @ ( complement @ ( converse @ top ) ) @ ( composition @ top @ ( complement @ ( composition @ top @ top ) ) ) )
= ( complement @ ( converse @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl4436,zip_derived_cl137]) ).
thf(zip_derived_cl1367_048,plain,
( top
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1346,zip_derived_cl579]) ).
thf(zip_derived_cl117_049,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl114,zip_derived_cl12]) ).
thf(zip_derived_cl277_050,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl276,zip_derived_cl227,zip_derived_cl232]) ).
thf(zip_derived_cl157_051,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl3]) ).
thf(zip_derived_cl296,plain,
! [X0: $i] :
( X0
= ( join @ ( meet @ X0 @ ( complement @ X0 ) ) @ ( complement @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl277,zip_derived_cl157]) ).
thf(zip_derived_cl12_052,plain,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_zero]) ).
thf(zip_derived_cl307,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl296,zip_derived_cl12]) ).
thf(zip_derived_cl307_053,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl296,zip_derived_cl12]) ).
thf(zip_derived_cl117_054,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl114,zip_derived_cl12]) ).
thf(zip_derived_cl3_055,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl138,plain,
! [X0: $i] :
( ( meet @ top @ X0 )
= ( complement @ ( join @ zero @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl117,zip_derived_cl3]) ).
thf(zip_derived_cl1063,plain,
! [X0: $i] :
( ( meet @ top @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl307,zip_derived_cl138]) ).
thf(zip_derived_cl307_056,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl296,zip_derived_cl12]) ).
thf(zip_derived_cl11_057,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl0_058,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl1_059,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[maddux2_join_associativity]) ).
thf(zip_derived_cl36,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X1 @ X0 ) @ X2 ) ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl1]) ).
thf(zip_derived_cl1472,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ X1 ) @ ( join @ X1 @ X0 ) )
= ( join @ top @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl36]) ).
thf(zip_derived_cl1354_060,plain,
! [X0: $i] :
( ( join @ top @ X0 )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1346,zip_derived_cl0]) ).
thf(zip_derived_cl1499,plain,
! [X0: $i,X1: $i] :
( ( join @ ( complement @ X1 ) @ ( join @ X1 @ X0 ) )
= top ),
inference(demod,[status(thm)],[zip_derived_cl1472,zip_derived_cl1354]) ).
thf(zip_derived_cl2233,plain,
! [X0: $i] :
( ( join @ ( complement @ zero ) @ X0 )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl307,zip_derived_cl1499]) ).
thf(zip_derived_cl277_061,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl276,zip_derived_cl227,zip_derived_cl232]) ).
thf(zip_derived_cl2308,plain,
( top
= ( complement @ zero ) ),
inference('sup+',[status(thm)],[zip_derived_cl2233,zip_derived_cl277]) ).
thf(zip_derived_cl3_062,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl2336,plain,
! [X0: $i] :
( ( meet @ X0 @ zero )
= ( complement @ ( join @ ( complement @ X0 ) @ top ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2308,zip_derived_cl3]) ).
thf(zip_derived_cl1346_063,plain,
! [X0: $i] :
( ( join @ X0 @ top )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1299,zip_derived_cl35]) ).
thf(zip_derived_cl117_064,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl114,zip_derived_cl12]) ).
thf(zip_derived_cl2350,plain,
! [X0: $i] :
( ( meet @ X0 @ zero )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl2336,zip_derived_cl1346,zip_derived_cl117]) ).
thf(zip_derived_cl157_065,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl3]) ).
thf(zip_derived_cl2683,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( join @ ( complement @ X0 ) @ zero ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl2350,zip_derived_cl157]) ).
thf(zip_derived_cl0_066,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl138_067,plain,
! [X0: $i] :
( ( meet @ top @ X0 )
= ( complement @ ( join @ zero @ ( complement @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl117,zip_derived_cl3]) ).
thf(zip_derived_cl2690,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( meet @ top @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2683,zip_derived_cl0,zip_derived_cl138]) ).
thf(zip_derived_cl3315,plain,
! [X0: $i] :
( ( complement @ X0 )
= ( join @ zero @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1063,zip_derived_cl2690]) ).
thf(zip_derived_cl307_068,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl296,zip_derived_cl12]) ).
thf(zip_derived_cl3491,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3315,zip_derived_cl307]) ).
thf(zip_derived_cl3506,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl307,zip_derived_cl3491]) ).
thf(zip_derived_cl1367_069,plain,
( top
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1346,zip_derived_cl579]) ).
thf(zip_derived_cl117_070,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl114,zip_derived_cl12]) ).
thf(zip_derived_cl8371,plain,
( ( composition @ top @ ( complement @ ( composition @ top @ top ) ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl8328,zip_derived_cl1367,zip_derived_cl117,zip_derived_cl3506,zip_derived_cl1367,zip_derived_cl117]) ).
thf(composition_distributivity,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( composition @ ( join @ X0 @ X1 ) @ X2 )
= ( join @ ( composition @ X0 @ X2 ) @ ( composition @ X1 @ X2 ) ) ) ).
thf(zip_derived_cl6,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( composition @ ( join @ X0 @ X2 ) @ X1 )
= ( join @ ( composition @ X0 @ X1 ) @ ( composition @ X2 @ X1 ) ) ),
inference(cnf,[status(esa)],[composition_distributivity]) ).
thf(zip_derived_cl8837,plain,
! [X0: $i] :
( ( composition @ ( join @ top @ X0 ) @ ( complement @ ( composition @ top @ top ) ) )
= ( join @ zero @ ( composition @ X0 @ ( complement @ ( composition @ top @ top ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl8371,zip_derived_cl6]) ).
thf(zip_derived_cl1354_071,plain,
! [X0: $i] :
( ( join @ top @ X0 )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl1346,zip_derived_cl0]) ).
thf(zip_derived_cl8371_072,plain,
( ( composition @ top @ ( complement @ ( composition @ top @ top ) ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl8328,zip_derived_cl1367,zip_derived_cl117,zip_derived_cl3506,zip_derived_cl1367,zip_derived_cl117]) ).
thf(zip_derived_cl3506_073,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl307,zip_derived_cl3491]) ).
thf(zip_derived_cl8849,plain,
! [X0: $i] :
( zero
= ( composition @ X0 @ ( complement @ ( composition @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl8837,zip_derived_cl1354,zip_derived_cl8371,zip_derived_cl3506]) ).
thf(zip_derived_cl4_074,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
= ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ),
inference(cnf,[status(esa)],[composition_associativity]) ).
thf(zip_derived_cl8928,plain,
! [X0: $i,X1: $i] :
( ( composition @ X1 @ ( composition @ X0 @ ( complement @ ( composition @ top @ top ) ) ) )
= zero ),
inference('sup+',[status(thm)],[zip_derived_cl8849,zip_derived_cl4]) ).
thf(zip_derived_cl8849_075,plain,
! [X0: $i] :
( zero
= ( composition @ X0 @ ( complement @ ( composition @ top @ top ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl8837,zip_derived_cl1354,zip_derived_cl8371,zip_derived_cl3506]) ).
thf(zip_derived_cl8957,plain,
! [X1: $i] :
( ( composition @ X1 @ zero )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl8928,zip_derived_cl8849]) ).
thf(zip_derived_cl25_076,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ ( converse @ X0 ) @ X1 ) )
= ( composition @ ( converse @ X1 ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl9]) ).
thf(zip_derived_cl8988,plain,
! [X0: $i] :
( ( converse @ zero )
= ( composition @ ( converse @ zero ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl8957,zip_derived_cl25]) ).
thf(zip_derived_cl3506_077,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl307,zip_derived_cl3491]) ).
thf(zip_derived_cl11_078,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
inference(cnf,[status(esa)],[def_top]) ).
thf(zip_derived_cl24_079,plain,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ ( converse @ X0 ) @ X1 ) )
= ( join @ X0 @ ( converse @ X1 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl7,zip_derived_cl8]) ).
thf(zip_derived_cl76,plain,
! [X0: $i] :
( ( converse @ top )
= ( join @ X0 @ ( converse @ ( complement @ ( converse @ X0 ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl11,zip_derived_cl24]) ).
thf(zip_derived_cl1367_080,plain,
( top
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1346,zip_derived_cl579]) ).
thf(zip_derived_cl1377,plain,
! [X0: $i] :
( top
= ( join @ X0 @ ( converse @ ( complement @ ( converse @ X0 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl76,zip_derived_cl1367]) ).
thf(zip_derived_cl3649,plain,
( top
= ( converse @ ( complement @ ( converse @ zero ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3506,zip_derived_cl1377]) ).
thf(zip_derived_cl7_081,plain,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
inference(cnf,[status(esa)],[converse_idempotence]) ).
thf(zip_derived_cl3861,plain,
( ( converse @ top )
= ( complement @ ( converse @ zero ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3649,zip_derived_cl7]) ).
thf(zip_derived_cl1367_082,plain,
( top
= ( converse @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl1346,zip_derived_cl579]) ).
thf(zip_derived_cl3900,plain,
( top
= ( complement @ ( converse @ zero ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3861,zip_derived_cl1367]) ).
thf(zip_derived_cl3491_083,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3315,zip_derived_cl307]) ).
thf(zip_derived_cl3944,plain,
( ( converse @ zero )
= ( complement @ top ) ),
inference('sup+',[status(thm)],[zip_derived_cl3900,zip_derived_cl3491]) ).
thf(zip_derived_cl117_084,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl114,zip_derived_cl12]) ).
thf(zip_derived_cl3956,plain,
( ( converse @ zero )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl3944,zip_derived_cl117]) ).
thf(zip_derived_cl3956_085,plain,
( ( converse @ zero )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl3944,zip_derived_cl117]) ).
thf(zip_derived_cl9011,plain,
! [X0: $i] :
( zero
= ( composition @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl8988,zip_derived_cl3956,zip_derived_cl3956]) ).
thf(zip_derived_cl277_086,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl276,zip_derived_cl227,zip_derived_cl232]) ).
thf(zip_derived_cl3_087,plain,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
inference(cnf,[status(esa)],[maddux4_definiton_of_meet]) ).
thf(zip_derived_cl298,plain,
! [X0: $i] :
( ( meet @ X0 @ X0 )
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl277,zip_derived_cl3]) ).
thf(zip_derived_cl3491_088,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3315,zip_derived_cl307]) ).
thf(zip_derived_cl3505,plain,
! [X0: $i] :
( ( meet @ X0 @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl298,zip_derived_cl3491]) ).
thf(zip_derived_cl157_089,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl3]) ).
thf(zip_derived_cl3604,plain,
! [X0: $i] :
( X0
= ( join @ X0 @ ( complement @ ( join @ ( complement @ X0 ) @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3505,zip_derived_cl157]) ).
thf(zip_derived_cl307_090,plain,
! [X0: $i] :
( X0
= ( join @ zero @ ( complement @ ( complement @ X0 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl296,zip_derived_cl12]) ).
thf(zip_derived_cl1731_091,plain,
! [X0: $i,X1: $i] :
( ( join @ X0 @ ( join @ X1 @ ( complement @ X0 ) ) )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl0,zip_derived_cl1716]) ).
thf(zip_derived_cl3008,plain,
! [X0: $i] :
( ( join @ ( complement @ X0 ) @ X0 )
= top ),
inference('sup+',[status(thm)],[zip_derived_cl307,zip_derived_cl1731]) ).
thf(zip_derived_cl117_092,plain,
( zero
= ( complement @ top ) ),
inference(demod,[status(thm)],[zip_derived_cl114,zip_derived_cl12]) ).
thf(zip_derived_cl3614,plain,
! [X0: $i] :
( X0
= ( join @ X0 @ zero ) ),
inference(demod,[status(thm)],[zip_derived_cl3604,zip_derived_cl3008,zip_derived_cl117]) ).
thf(zip_derived_cl3988_093,plain,
( ( meet @ sk__2 @ ( composition @ ( complement @ sk_ ) @ sk__1 ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl3978,zip_derived_cl117]) ).
thf(zip_derived_cl9011_094,plain,
! [X0: $i] :
( zero
= ( composition @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl8988,zip_derived_cl3956,zip_derived_cl3956]) ).
thf(zip_derived_cl31711,plain,
( ( meet @ ( complement @ sk_ ) @ ( composition @ sk__2 @ ( converse @ sk__1 ) ) )
= zero ),
inference(demod,[status(thm)],[zip_derived_cl31533,zip_derived_cl6063,zip_derived_cl9011,zip_derived_cl3614,zip_derived_cl3988,zip_derived_cl9011]) ).
thf(zip_derived_cl157_095,plain,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( meet @ X0 @ X1 ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl3]) ).
thf(zip_derived_cl48398,plain,
( ( complement @ sk_ )
= ( join @ zero @ ( complement @ ( join @ ( complement @ ( complement @ sk_ ) ) @ ( composition @ sk__2 @ ( converse @ sk__1 ) ) ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl31711,zip_derived_cl157]) ).
thf(zip_derived_cl3491_096,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3315,zip_derived_cl307]) ).
thf(zip_derived_cl3506_097,plain,
! [X0: $i] :
( X0
= ( join @ zero @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl307,zip_derived_cl3491]) ).
thf(zip_derived_cl48431,plain,
( ( complement @ sk_ )
= ( complement @ ( join @ sk_ @ ( composition @ sk__2 @ ( converse @ sk__1 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl48398,zip_derived_cl3491,zip_derived_cl3506]) ).
thf(zip_derived_cl3491_098,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3315,zip_derived_cl307]) ).
thf(zip_derived_cl52129,plain,
( ( join @ sk_ @ ( composition @ sk__2 @ ( converse @ sk__1 ) ) )
= ( complement @ ( complement @ sk_ ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl48431,zip_derived_cl3491]) ).
thf(zip_derived_cl3491_099,plain,
! [X0: $i] :
( X0
= ( complement @ ( complement @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3315,zip_derived_cl307]) ).
thf(zip_derived_cl52194,plain,
( ( join @ sk_ @ ( composition @ sk__2 @ ( converse @ sk__1 ) ) )
= sk_ ),
inference(demod,[status(thm)],[zip_derived_cl52129,zip_derived_cl3491]) ).
thf(zip_derived_cl17,plain,
( ( join @ ( composition @ sk__2 @ ( converse @ sk__1 ) ) @ sk_ )
!= sk_ ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0_100,plain,
! [X0: $i,X1: $i] :
( ( join @ X1 @ X0 )
= ( join @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[maddux1_join_commutativity]) ).
thf(zip_derived_cl20,plain,
( ( join @ sk_ @ ( composition @ sk__2 @ ( converse @ sk__1 ) ) )
!= sk_ ),
inference(demod,[status(thm)],[zip_derived_cl17,zip_derived_cl0]) ).
thf(zip_derived_cl52195,plain,
$false,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl52194,zip_derived_cl20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : REL044+2 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.GKeEiOTyDp true
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 20:01:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.20/0.65 % Total configuration time : 435
% 0.20/0.65 % Estimated wc time : 1092
% 0.20/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.97/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.97/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.97/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.97/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.97/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.97/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.97/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 76.18/11.57 % Solved by fo/fo5.sh.
% 76.18/11.57 % done 3333 iterations in 10.787s
% 76.18/11.57 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 76.18/11.57 % SZS output start Refutation
% See solution above
% 76.18/11.57
% 76.18/11.57
% 76.18/11.57 % Terminating...
% 77.25/11.69 % Runner terminated.
% 77.25/11.70 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------